A hiperbolic sine procedure for the spectrophotometric evaluation of acidity constants for two-step overlapping equilibria

An equation relating the absorbance of the solute to the acidity constants (pK (a1) and pK (a2)) and pH is derived for weak diprotic acids (diprotic bases and zwitterions). The equation is applicable in those cases in which the limiting absorbance of the species HR is intermediate between that of R and H (2) R. The evaluation of acidity constants for two-step overlapping equilibria from spectrophotometric measurements may be carried out in this way by linear plotting. The task is solving via a hyperbolic sine linearization of the absorbance versus pH graph. The procedure has been tested with the benzidine system and found to give good results. The equation derived could also be applied to other additive properties such as chromatographic retention factors, electrophoretic mobilities, NMR chemical shifts, fluorescence measurements, or hyperpolarizability.